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fromDual -- ideal from inverse system

Synopsis

Description

For other examples, and a more precise definition, see inverse systems.
i1 : R = ZZ/32003[x_1..x_3];
i2 : g = random(R^1, R^{-4})

o2 = | 1607x_1^4+6895x_1^3x_2-10246x_1^2x_2^2+5569x_1x_2^3+2680x_2^4+6813x_1^
     ------------------------------------------------------------------------
     3x_3+3785x_1^2x_2x_3+8646x_1x_2^2x_3+1239x_2^3x_3-11272x_1^2x_3^2+10892x
     ------------------------------------------------------------------------
     _1x_2x_3^2-13855x_2^2x_3^2-8142x_1x_3^3+10203x_2x_3^3+1902x_3^4 |

             1       1
o2 : Matrix R  <--- R
i3 : f = fromDual g

o3 = | x_2^2x_3-14406x_1x_3^2+11382x_2x_3^2+1777x_3^3
     ------------------------------------------------------------------------
     x_1x_2x_3+1839x_1x_3^2+769x_2x_3^2+11128x_3^3
     ------------------------------------------------------------------------
     x_1^2x_3-5695x_1x_3^2+5709x_2x_3^2+3876x_3^3
     ------------------------------------------------------------------------
     x_2^3+8565x_1x_3^2+14302x_2x_3^2-6792x_3^3
     ------------------------------------------------------------------------
     x_1x_2^2-14848x_1x_3^2-10750x_2x_3^2-11451x_3^3
     ------------------------------------------------------------------------
     x_1^2x_2+5751x_1x_3^2-2337x_2x_3^2+6227x_3^3
     ------------------------------------------------------------------------
     x_1^3-12969x_1x_3^2+6964x_2x_3^2+10955x_3^3 |

             1       7
o3 : Matrix R  <--- R
i4 : res ideal f

      1      7      7      1
o4 = R  <-- R  <-- R  <-- R  <-- 0
                                  
     0      1      2      3      4

o4 : ChainComplex
i5 : betti oo

            0 1 2 3
o5 = total: 1 7 7 1
         0: 1 . . .
         1: . . . .
         2: . 7 7 .
         3: . . . .
         4: . . . 1

o5 : BettiTally

See also

Ways to use fromDual :